The invention finds its application notably in all systems which require a significant degree of spatial resolution [(environments with a large number of transmitters, array with a low number of sensors, significant residual model errors (standardization, calibration, etc.), etc.)].
At the start of the 80s, numerous order 2 direction finding procedures termed high-resolution (HR) [1] [14] were developed to alleviate the limitations of procedures that were termed super resolution [2-3] in relation to weak sources. Among these HR procedures, the so-called subspace procedures such as the MUSIC (or MUSIC-2) procedure [14] are the most popular. These HR procedures are very efficacious in a multi-source context insofar as they possess, in the absence of model errors and for background noise of known spatial coherence, unlimited asymptotic separating ability whatever the signal-to-noise ratio (SNR) of the sources. However, these HR procedures suffer from serious drawbacks. Specifically, they can process at most N−1 noncoherent sources on the basis of an array with N antennas and are not very robust either to model errors [10] [15], which are inherent in operational implementations, or to the presence of background noise of unknown spatial coherence [12], typical of the HF range for example. Furthermore, their performance can become greatly affected when this involves separating several weak and angularly close sources on the basis of a limited number of observed samples.
From the end of the 80s, mainly to alleviate the previous limitations, order 4 high-resolution direction finding procedures [13] have been developed for non-Gaussian sources, that are omnipresent in radiocommunications, among which the extension of the MUSIC procedure to order 4 [13], called MUSIC-4, is the most popular. Specifically, the order 4 procedures are asymptotically robust to the presence of Gaussian noise of unknown spatial coherence [13]. Furthermore, in spite of their greater variance, they generate a virtual increase in the aperture of the array and the number of antennas, introducing the notion of virtual array (RV) to order 4 [4] [6] and offering increased resolution and the possibility of processing a greater number of sources than the number of antennas. In particular, on the basis of an array with N antennas, the MUSIC-4 procedure can process up to N(N−1)+1 sources when the antennas are identical and up to (N+1)(N−1) sources for different antennas.